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Nanocarbons have been catalytically grown since 1993. However, even today, the formation mechanisms of carbon nanotubes (CNTs) and graphene are not sufficiently understood. This sustained challenge has been an engine for the development in theory concepts and computational methods, tackling the problem of well-controlled production of these nanomaterials. This article discusses how experimental discoveries and theoretical approaches evolved hand-in-hand for the successful understanding of challenging issues, highlighting parallels and distinctions between graphene and CNTs. Key aspects include the mechanisms of nucleation and CNT-liftoff, chiral symmetry selection and control, rates of growth and island shapes, mechanisms defining single chirality of the nanotubes, and ways to suppress grain boundaries in the quest for ever larger and faster growing single-crystal graphene, or longest defect-free CNTs. The theme of catalyst chemistry and structure, either as a nanoparticle or a planar substrate, is traced through the stages of nanocarbon formation, with focus on theoretically generalizable findings.